Particle propagation in a random and quasiperiodic potential

TL;DR

This paper numerically studies the Anderson transition in various dimensions for a particle in random and quasiperiodic potentials, revealing critical exponents that differ from standard scaling theories.

Contribution

It provides new insights into the critical behavior of the Anderson transition in higher dimensions with non-standard critical exponents.

Findings

Critical exponents differ from standard scaling predictions.

The transition behavior varies with effective dimension.

Possible reasons for deviations are discussed.

Abstract

We numerically investigate the Anderson transition in an effective dimension $d$ ($3 \leq d \leq 11$) for one particle propagation in a model random and quasiperiodic potential. The found critical exponents are different from the standard scaling picture. We discuss possible reasons for this difference.